Related Experiment Video
Updated: Aug 17, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Extension of the BLOCH T(3/2) law to magnetic nanostructures: Bose-Einstein condensation
E Della Torre1, L H Bennett, R E Watson
1Electrical and Computer Engineering Department, George Washington University, Washington, D.C. 20052, USA.
Abstract:
We report a newly observed phenomenon, namely, the observation of a visible anomaly in the Bloch T(3/2) law for the temperature dependence of magnetization of nanostructured ferromagnets, for which we give a thermodynamic explanation. Our interpretation extends the Bloch law by introducing the system's chemical potential and assumes a finite Bose-Einstein condensation temperature T(BE) of the magnons. Our extension involves accounting for the possibility of a magnon or magnetic entropy term, leading to a magnon chemical potential (hitherto omitted in the traditional derivation) which varies with temperature. The result is a subtle upturn of the magnetization curves of ferromagnetic nanoparticles in the 10 to 50 K temperature range. Here we show experimental data for nanomaterials and an outline of the extended theory which includes T(BE).
Related Concept Videos
Atomic Nuclei: Nuclear Relaxation Processes
Magnetic Moment of an Electron
Atomic Nuclei: Nuclear Spin State Population Distribution
Diamagnetic Shielding of Nuclei: Local Diamagnetic Current
Atomic Nuclei: Nuclear Magnetic Moment
Magnetic Field due to Moving Charges
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
